Seminars in Taipei, October 2002

Seminars given in Taipei will relate to my recent work on “Mathematical Growth from Child to Mathematician” which traces the cognitive development of mathematical thinking through the development of the individual.

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Monday, October 14th, 2002: The Theory of Procepts
This theory (begun in 1991 with Eddie Gray) considers the subtle ways in which symbols in arithmetic, algebra and calculus are interpreted both as process and concept.
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Other reading:
Thomas, M. O. J. & Tall, D. O. (2001). The long-term cognitive development of symbolic algebra, International Congress of Mathematical Instruction (ICMI) Working Group Proceedings - The Future of the Teaching and Learning of Algebra, Melbourne, 2, 590-597.
David Tall, Eddie Gray, Maselan Bin Ali, Lillie Crowley, Phil DeMarois, Mercedes McGowen, Demetra Pitta, Marcia Pinto, Michael Thomas, and Yudariah Yusof (2001): Symbols and the Bifurcation between Procedural and Conceptual Thinking, Canadian Journal of Science, Mathematics and Technology Education 1, 81–104.

Monday, October 21st, 2002: Three worlds of Mathematics
This recent development in my perspective of how we develop mathematical thinking relates a categorization of our growing mathematical thinking process in what I term the EMBODIED, SYMBOLIC & FORMAL mathematical worlds.
Download overheads (692k)

Other reading:
The theory began its development in Mathematical Growth in Elementary and Advanced Mathematical Thinking, plenary address at PME in 1995.
The latest developments were applied to calculus in Three Worlds of Mathematics in the Calculus, as presented in Rio, February, 2002
and The relationship between Physical Embodiment and Mathematical Symbolism: The Concept of Vector, (with Anna Watson and Takis Spirou) written September 2002 and applying the ‘ three worlds’ to the case of vectors.

October 31, 2002, (National Taiwan Normal University, Science Education Department):
How the Biological Brain affects the Mathematical Mind using Visual and Symbolic Ideas.
This is a modified version of an earlier talk redrafted for a shorter seminar with science education students.

November 7th 2002, (National Taiwan Normal University, Science Education Department):
The relationship between physical embodiment and mathematical symbolism: the concepts of force and vector.
This talk is based on The Relationship between Physical Embodiment and Mathematical Symbolism: The Concept of Vector, (with Anna Watson and Takis Spirou), written September 2002.

last modified: Sunday, January 26, 2003